Your kart may not have had axle spacers but I think they are a good idea, critical even, for long term bearing life. They're actually
bearing spacers and are extremely important to take the side load off your bearings.
https://www.diygokarts.com/community/threads/gokart-wheel-bearings-and-pipe.47110/
I think Ken-Bar (and Carter Brothers, the manufacturer most similar to Ken-Bar) may not have used bearing spacers because they may have deemed them unnecessary or superfluous. Bearing spacers don't show up on the Carter Brothers exploded parts diagrams for instance. Both manufacturers used a separate hub that the two-piece rims bolted to.
I'm used to seeing bearing spacers on the two-piece wheels (Manco wheels, Azusa Tri-Stars, Azusalites, etc) that hold a bearing in each half. The bearing spacers may be more of a necessity on those wheels, I'm not sure.
As for what to put on the axle spindles and in what order, we can use the Manco illustration below as a guide. I think manufacturers kept it extremely simple so there was less parts to lose. You can use flat washers and lock washers but most manufacturers didn’t.
Moving right to left:
#40 Spacer, 5/8 ID x 1/4" thick
#22 Bearing
#24 Nut, 1/4-20
#26 Wheel Half
#25 Spanner
#26 Wheel Half
#23 Bolt, 1/4-20 x 3/4"
#22 Bearing
#21 Nut, 5/8-11 Toplock
The #40 spacer (a real axle spacer) may be a crucial part as it commonly prevents the bearing from fouling on the inner end of the #43 spindle that usually has a weld blob there and also helps prevent the tire rubbing on the spindle and the "C" bracket. This axle spacer may also take up room (especially if you're using narrow wheels) on the spindle so you don't run out of threads for the #21 Toplock Nut before it seats against the wheel bearing. The Toplock nut takes the place of a lock washer and is better IMO than a Nylock nut or lock washers. Just makes it neater.